Reductions of Darboux transformations for the PT-symmetric nonlocal Davey-Stewartson equations

In this letter, a study of the reductions of the Darboux transformations (DTs) for the PT-symmetric nonlocal Davey-Stewartson (DS) equations is presented. Firstly, a binary DT is constructed in integral form for the PT-symmetric nonlocal DS-I equation. Secondly, an elementary DT is constructed in differential form for the PT-symmetric nonlocal DS-II equation. Afterwards, a new binary DT in integral form is also found for the nonlocal DS-II equation. Moreover, it is shown that the symmetry properties in the corresponding Lax-pairs of the equations are well preserved through these DTs. Thirdly, based on above DTs, the fundamental rogue waves and rational travelling waves are obtained. (C) 2018 Elsevier Ltd. All rights reserved.